There is the regular method to find the transformation matrix \(S\)  as the \(1/\omega _0\)  expansion (the Floquet-Magnus expansion) [1]}, [2]}, [3]}, [4]}. Keeping the first three terms in the expansion, the effective stationary Hamiltonian (REF ) reads

Heff=H0+n=1[Hn,H-n]n0
